Speaker: Jeff Giansiracusa (Oxford)

Title: Teichmuller theory for the Deligne-Mumford compactification

Abstract: It is well known that the moduli stack of smooth curves is homotopy equivalent to the classifying space of the mapping class group; this follows immediately from the contractibility of Teichmuller space. I will describe the generalisation of this statement to the Deligne-Mumford compactified moduli stack of stable curves. Now the homotopy type is that of the classifying space (or nerve) of a category built from mapping class groups of stable nodal topological surfaces. The main ingredient is a Teichmuller-theoretic description of the moduli stack of stable curves that was constructed by Bers in the 1970s.